Highly-spectrally-efficient transmission using orthogonal frequency division multiplexing

ABSTRACT

A transmitter may map, using a selected modulation constellation, each of C′ bit sequences to a respective one of C′ symbols, where C′ is a number greater than one. The transmitter may process the C′ symbols to generate C′ inter-carrier correlated virtual subcarrier values. The transmitter may decimate the C′ virtual subcarrier values down to C physical subcarrier values, C being a number less than C′. The transmitter may transmit the C physical subcarrier values on C orthogonal frequency division multiplexed (OFDM) subcarriers. The modulation constellation may be an N-QAM constellation, where N is an integer. The processing may comprise filtering the C′ symbols using an array of C′ filter tap coefficients. The filtering may comprise cyclic filtering. The filtering may comprise multiplication by a circulant matrix populated with the C′ filter tap coefficients.

CLAIM OF PRIORITY

This patent application makes reference to, claims priority to andclaims benefit from:

-   U.S. Provisional Patent Application Ser. No. 61/662,085 titled    “Apparatus and Method for Efficient Utilization of Bandwidth” and    filed on Jun. 20, 2012;-   U.S. Provisional Patent Application Ser. No. 61/726,099 titled    “Modulation Scheme Based on Partial Response” and filed on Nov. 14,    2012;-   U.S. Provisional Patent Application Ser. No. 61/729,774 titled    “Modulation Scheme Based on Partial Response” and filed on Nov. 26,    2012;-   U.S. Provisional Patent Application Ser. No. 61/747,132 titled    “Modulation Scheme Based on Partial Response” and filed on Dec. 28,    2012;-   U.S. Provisional Patent Application Ser. No. 61/768,532 titled “High    Spectral Efficiency over Non-Linear, AWGN Channels” and filed on    Feb. 24, 2013; and-   U.S. Provisional Patent Application Ser. No. 61/807,813 titled “High    Spectral Efficiency over Non-Linear, AWGN Channels” and filed on    Apr. 3, 2013.

This application is also a continuation-in-part of U.S. patentapplication Ser. No. 13/755,008 titled “Dynamic Filter Adjustment forHighly-Spectrally-Efficient Communications” and filed on Jan. 31, 2013.

Each of the above applications is hereby incorporated herein byreference in its entirety.

INCORPORATIONS BY REFERENCE

This patent application makes reference to:

-   U.S. patent application Ser. No. 13/754,964, titled “Low-Complexity,    Highly-Spectrally-Efficient Communications,” and filed on Jan. 31,    2013, now patented as U.S. Pat. No. 8,582,637;-   U.S. patent application Ser. No. 13/754,998, titled “Design and    Optimization of Partial Response Pulse Shape Filter,” and filed on    Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,001, titled “Constellation    Map Optimization for Highly Spectrally Efficient Communications,”    and filed on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,008, titled “Dynamic Filter    Adjustment for Highly-Spectrally-Efficient Communications,” and    filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,571,131;-   U.S. patent application Ser. No. 13/755,011, titled “Timing    Synchronization for Reception of Highly-Spectrally-Efficient    Communications,” and filed on Jan. 31, 2013, now patented as U.S.    Pat. No. 8,559,494;-   U.S. patent application Ser. No. 13/755,014, titled “Signal    Reception Using Non-Linearity-Compensated, Partial Response    Feedback,” and filed on Jan. 31, 2013, now patented as U.S. Pat. No.    8,559,496;-   U.S. patent application Ser. No. 13/755,018, titled “Feed Forward    Equalization for Highly-Spectrally-Efficient Communications,” and    filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,599,914;-   U.S. patent application Ser. No. 13/755,021, titled “Decision    Feedback Equalizer for Highly Spectrally Efficient Communications,”    and filed on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,025, titled “Decision    Feedback Equalizer with Multiple Cores for    Highly-Spectrally-Efficient Communications,” and filed on Jan. 31,    2013;-   U.S. patent application Ser. No. 13/755,026, titled “Decision    Feedback Equalizer Utilizing Symbol Error Rate Biased Adaptation    Function for Highly Spectrally Efficient Communications,” and filed    on Jan. 31, 2013, now patented as U.S. Pat. No. 8,559,498;-   U.S. patent application Ser. No. 13/755,028, titled “Coarse Phase    Estimation For Highly-Spectrally-Efficient Communications,” and    filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,548,097;-   U.S. patent application Ser. No. 13/755,039, titled “Fine Phase    Estimation for Highly Spectrally Efficient Communications,” and    filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,565,363;-   U.S. patent application Ser. No. 13/755,972, titled “Multi-Mode    Transmitter for Highly-Spectrally-Efficient Communications,” and    filed on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,043, titled “Joint Sequence    Estimation of Symbol and Phase With High Tolerance Of Nonlinearity,”    and filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,605,832;-   U.S. patent application Ser. No. 13/755,050, titled “Adaptive    Non-Linear Model for Highly-Spectrally-Efficient Communications,”    and filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,553,821;-   U.S. patent application Ser. No. 13/755,052, titled “Pilot    Symbol-Aided Sequence Estimation for Highly-Spectrally-Efficient    Communications,” and filed on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,054, titled “Method and    System for Corrupt Symbol Handling for Providing High Reliability    Sequences,” and filed on Jan. 31, 2013, now patented as U.S. Pat.    No. 8,571,146;-   U.S. patent application Ser. No. 13/755,060, titled “Method and    System for Forward Error Correction Decoding with Parity Check for    Use in Low Complexity Highly-spectrally-efficient Communications,”    and filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,566,687;-   U.S. patent application Ser. No. 13/755,061, titled “Method and    System for Quality of Service (QoS) Awareness in a Single Channel    Communication System,” and filed on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/756,079, titled “Pilot Symbol    Generation for Highly-Spectrally-Efficient Communications,” and    filed on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,065, titled “Timing Pilot    Generation for Highly-Spectrally-Efficient Communications,” and    filed on Jan. 31, 2013, now patented as U.S. Pat. No. 8,548,072;-   U.S. patent application Ser. No. 13/756,010, titled “Multi-Mode    Receiver for Highly-Spectrally-Efficient Communications,” and filed    on Jan. 31, 2013;-   U.S. patent application Ser. No. 13/755,068, titled “Forward Error    Correction with Parity Check Encoding for use in Low Complexity    Highly-spectrally-efficient Communications,” and filed on Jan. 31,    2013, now patented as U.S. Pat. No. 8,572,458;-   U.S. patent application Ser. No. 13/756,469, titled    “Highly-Spectrally-Efficient Receiver,” and filed on Jan. 31, 2013,    now patented as U.S. Pat. No. 8,526,523;-   U.S. patent application Ser. No. 13/921,665, titled    “Highly-Spectrally-Efficient Reception Using Orthogonal Frequency    Division Multiplexing,” and filed on the same date as this    application;-   U.S. patent application Ser. No. 13/921,749, titled “Multi-Mode    Orthogonal Frequency Division Multiplexing Transmitter for    Highly-Spectrally-Efficient Communications,” and filed on the same    date as this application; and-   U.S. patent application Ser. No. 13/921,813, titled “Multi-Mode    Orthogonal Frequency Division Multiplexing Receiver for    Highly-Spectrally-Efficient Communications,” and filed on the same    date as this application.

Each of the above applications is hereby incorporated herein byreference in its entirety.

TECHNICAL FIELD

Aspects of the present application relate to electronic communications.

BACKGROUND

Existing communications methods and systems are overly power hungryand/or spectrally inefficient. Further limitations and disadvantages ofconventional and traditional approaches will become apparent to one ofskill in the art, through comparison of such approaches with someaspects of the present method and system set forth in the remainder ofthis disclosure with reference to the drawings.

BRIEF SUMMARY

Methods and systems are provided for highly-spectrally-efficientcommunications using orthogonal frequency division multiplexing,substantially as illustrated by and/or described in connection with atleast one of the figures, as set forth more completely in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a diagram of an example OFDM transmitter.

FIG. 1B depicts simulation results of an example cyclic filter for ahighly-spectrally-efficient OFDM transmitter.

FIG. 1C depicts a flowchart describing operation of an exampleimplementation of a highly-spectrally-efficient OFDM transmitter.

FIG. 2A is a diagram of an example OFDM receiver.

FIGS. 2B and 2C depict a flowchart describing operation of an exampleimplementation of a highly-spectrally-efficient OFDM receiver.

FIG. 2D depicts a flowchart describing operation of an example decodingcircuit of a highly-spectrally-efficient OFDM receiver.

FIG. 3 is a flowchart describing a process for mitigating the effects offrequency-selective fading in highly-spectrally-efficient OFDMcommunication system.

DETAILED DESCRIPTION

As utilized herein the terms “circuits” and “circuitry” refer tophysical electronic components (i.e. hardware) and any software and/orfirmware (“code”) which may configure the hardware, be executed by thehardware, and or otherwise be associated with the hardware. As usedherein, for example, a particular processor and memory may comprise afirst “circuit” when executing a first one or more lines of code and maycomprise a second “circuit” when executing a second one or more lines ofcode. As utilized herein, “and/or” means any one or more of the items inthe list joined by “and/or”. As an example, “x and/or y” means anyelement of the three-element set {(x), (y), (x, y)}. As another example,“x, y, and/or z” means any element of the seven-element set {(x), (y),(z), (x, y), (x, z), (y, z), (x, y, z)}. As utilized herein, the term“exemplary” means serving as a non-limiting example, instance, orillustration. As utilized herein, the terms “e.g.,” and “for example”set off lists of one or more non-limiting examples, instances, orillustrations. As utilized herein, circuitry is “operable” to perform afunction whenever the circuitry comprises the necessary hardware andcode (if any is necessary) to perform the function, regardless ofwhether performance of the function is disabled, or not enabled, by someuser-configurable setting.

Orthogonal Frequency Division Multiplexing (OFDM) has gained traction inrecent years in high-capacity wireless and wireline communicationsystems such as WiFi (IEEE Std 802.11n/ac), 3GPP-LTE, and G.hn. Oneadvantage of OFDM is that it can reduce the need for complicatedequalization over frequency selective channels. It is particularlypowerful in combination with multiple independent spatial streams andmultiple antennas, Multiple Input Multiple Output (MIMO) systems. Oneadvantage of OFDM is that it can reduce or eliminate the need forcomplicated equalization over frequency selective channels. ConventionalMIMO-OFDM solutions are based on suboptimal Zero Forcing, SIC(Successive Interference Cancellation), and minimum mean square error(MMSE) receivers. These detection algorithms are significantly inferiorto maximum likelihood (ML) and near-ML receivers. Lately, in emergingstandards, constellation size continues to increase (256-QAM, 1024-QAM,and so on). The associated ML state space of such solutions is N^(SS),where N and SS stand for the constellation size and total number of MIMOspatial streams, respectively. Consequently, aspects of this disclosurepertain to reduced state/complexity ML decoders that achieve highperformance.

Example implementations of the present disclosure may use relativelysmall constellations with partial response signaling that occupiesaround half the bandwidth of “ISI-free” or “full response” signaling.Thus, the ML state space is reduced significantly and cost effectivenessof reduced complexity ML detection is correspondingly improved.Additionally, aspects of this disclosure support detection in thepresence of phase noise and non-linear distortion without the need ofpilot symbols that reduce capacity and spectral efficiency. The spectralcompression also provides multidimensional signal representation thatimproves performance in an AWGN environment as compared to conventionaltwo-dimensional QAM systems. In accordance with an implementation ofthis disclosure, transmitter shaping filtering may be applied in thefrequency domain in order to preserve the independency of the OFDMsymbols.

FIG. 1A is a diagram of an example OFDM transmitter. The exampletransmitter 100 comprises a symbol mapper circuit 102, an inter-symbolcorrelation (ISC) generation circuit 104, a decimation circuit 108, aserial-to-parallel circuit 108, an inverse fast Fourier transform (IFFT)circuit 112, a parallel-to-serial circuit 114, a cyclic prefix andwindowing circuit 116, and a transmit front-end circuit 118. In theexample implementation shown, the transmitter transmits into a channel120.

The symbol mapper circuit 102, may be operable to map, according to aselected modulation scheme, bits of a bitstream to be transmitted(“Tx_bitstream”) to symbols. For example, for a quadrature amplitudemodulation (QAM) scheme having a symbol alphabet of N (N-QAM), themapper may map each Log₂(N) bits of the Tx_bitstream to a single symbolrepresented as a complex number and/or as in-phase (I) andquadrature-phase (Q) components. Although N-QAM is used for illustrationin this disclosure, aspects of this disclosure are applicable to anymodulation scheme (e.g., pulse amplitude modulation (PAM), amplitudeshift keying (ASK), phase shift keying (PSK), frequency shift keying(FSK), etc.). Additionally, points of the N-QAM constellation may beregularly spaced (“on-grid”) or irregularly spaced (“off-grid”).Furthermore, the symbol constellation used by the mapper 102 may beoptimized for best bit-error rate (BER) performance (or adjusted toachieve a target BER) that is related to log-likelihood ratio (LLR) andto optimizing mean mutual information bit (MMIB) (or achieving a targetMMIB). The Tx_bitstream may, for example, be the result of bits of datapassing through a forward error correction (FEC) encoder and/or aninterleaver. Additionally, or alternatively, the symbols out of themapper 102 may pass through an interleaver.

The ISC generation circuit 104 may be operable to filter the symbolsoutput by the mapper 102 to generate C′ virtual subcarrier values (theterminology “virtual subcarrier” is explained below) having asignificant, controlled amount inter-symbol correlation among symbols tobe output on different subcarriers (i.e., any particular one of the C′virtual subcarrier values may be correlated with a plurality of the C′symbols output by mapper 102). In other words, the inter-symbolcorrelation introduced by the ISC generation circuit may be correlationbetween symbols to be output on different subcarriers. In an exampleimplementation, the ISC generation circuit 104 may be a cyclic filter.

The response of the ISC generation circuit 104 may be determined by aplurality of coefficients, denoted p (where underlining indicates avector), which may be, for example, stored in memory 124. In an exampleimplementation, the ISC generation circuit 104 may perform a cyclic (or,equivalently, “circular”) convolution on sets of C′ symbols from themapper 102 to generate sets of C′ virtual subcarrier values conveyed assignal 105. In such an implementation, the ISC generation circuit 104may thus be described as a circulant matrix that multiplies an inputvector of C′ symbols by a C′×C′ matrix, where each row i+1 of the matrixmay be a circularly shifted version of row i of the matrix, i being aninteger from 1 to C′. For example, for C′=4 (an arbitrary value chosenfor illustration only) and p=[p1 p2 p3 p4], the matrix may be asfollows:

$\quad\begin{bmatrix}{p\; 1} & {p\; 2} & {p\; 3} & {p\; 4} \\{p\; 4} & {p\; 1} & {p\; 2} & {p\; 3} \\{p\; 3} & {p\; 4} & {p\; 1} & {p\; 2} \\{p\; 2} & {p\; 3} & {p\; 4} & {p\; 1}\end{bmatrix}$In another example, the length of p may be less than C′, and zeropadding may be used to fill the rows and/or columns to length C′ and/orpad the rows and/or columns. For example, C′ may be equal to 6 and thematrix above (with p having four elements) may be padded to create a sixelement vector p _(Z)=[p1 p2 p3 p4 0 0] and then p _(Z) may be used togenerate a 6 by 6 matrix in the same way that p was used to generate the4 by 4 matrix. As another example, only the rows may be padded such thatthe result is a C′×LP matrix, where LP is the length of p (e.g., a 4×6matrix in the above example). As another example, only the columns maybe padded such that the result is a LP×C′ matrix, where LP is the lengthof p (e.g., a 6×4 matrix in the above example).

The decimation circuit 108 may be operable to decimate groups of C′virtual subcarrier values down to C transmitted physical subcarriervalues (the term “physical subcarrier” is explained below). Accordingly,the decimation circuit 108 may be operable to perform downsamplingand/or upsampling. The decimation factor may be an integer or afraction. The output of the decimator 108 hence comprises C physicalsubcarrier values per OFDM symbol. The decimation may introducesignificant aliasing in case that the ISC generation circuit 104 doesnot confine the spectrum below the Nyquist frequency of the decimation.However, in example implementations of this disclosure, such aliasing isallowed and actually improves performance because it provides anadditional degree of freedom. The C physical subcarrier values may becommunicated using C of C+Δtotal subcarriers of the channel 120. Δmaycorrespond to the number of OFDM subcarriers on the channel 120 that arenot used for transmitting data. For example, data may not be transmitteda center subcarrier in order to reduce DC offset issues. As anotherexample, one or more subcarriers may be used as pilots to support phaseand frequency error corrections at the receiver. Additionally, zerosubcarrier padding may be used to increase the sampling rate thatseparates the sampling replicas and allow the use of low complexityanalog circuitry. The C+Δsubcarriers of channel 120 may be spaced atapproximately (e.g., within circuit tolerances) BW/(C+Δ) (according tothe Nyquist criterion) and with effective OFDM symbol duration of lessthan or equal to (C+Δ)/BW (according to the Nyquist criterion). Aspectsof the invention may, however, enable the receiver to recover theoriginal C′ symbols from the received OFDM symbol (Thus the reason forreferring to C′ as the number of “virtual subcarriers”). This deliveryof C′ symbols using C effective subcarriers of bandwidth BW/(C+Δ), andOFDM symbol timing of less than or equal to (C+Δ)/BW thus corresponds toa bandwidth reduction of (C′+Δ)/(C+Δ) or, equivalently, a symbol rateincrease of C′/C over conventional OFDM systems (assuming the samenumber, Δ, of unused subcarriers in the conventional system).

To reduce complexity, in an example implementation, the functionalitiesof 104 and 108 may be merged by calculating only a subset (C_(S)) of theC physical subcarriers subset from C′ by taking out the rows of thematrix that are related to the decimated virtual subcarriers of the ISCgenerating, C′×C′ matrix. For example, decimation of factor of 2 may beachieved by eliminating the even column vectors of the C′×C′ matrixdescribed in paragraph [0021] (assuming, for purposes of this example,that the information symbol vector (length of C′) is a row vector thatleft multiplies the matrix).

Generally speaking, in an example implementation wherein the circuit 104is a cyclic filter, methods and systems of designing the ISC generationcircuit 104 may be similar to methods and systems described in U.S.patent application Ser. No. 13/754,998 titled “Design and Optimizationof Partial Response Pulse Shape Filter,” which is incorporated byreference above. Similar to the design of the filter(s) in thesingle-carrier case described in U.S. patent application Ser. No.13/754,998, the design of a cyclic filter implementation of the circuit104 may be based on using the symbol error rate (SER) union bound as acost function and may aim to maximize the Euclidean distance associatedwith one or more identified error patterns. Using a shaping filtercharacterized by the coefficients p, the distance induced by errorpattern ε may be expressed as:δ²(ε, p )=Σ_(n)|Σ_(k) p _([n-k])ε_([k])|²=Σ_(k)Σ_(l)ε_([k])ε*_([l])Σ_(n)p _([n-k]) p* _([n-l])  Eq. 1AAssuming, for purposes of illustration, a spectral compression factor 2,then, after decimation by 2, EQ. 1A becomes:δ₂ ²(ε, p )=Σ_(n)|Σ_(k) p _([2n-k])ε_([k])|²=Σ_(n)|Σ_(k)ε_([2n-2k]) p_([2k])+Σ_(k)ε_([2n-2k+1]) p _([2k−1])|²  Eq. 1BWhere the right-hand-side summation relates to odd-indexed symbols andthe left-hand-side summation relates to even-indexed symbols. Eq. 1B maythen be rewritten as:

$\begin{matrix}{{\delta_{2}^{2}\left( {\underset{\_}{\varepsilon},\underset{\_}{p}} \right)} = {\sum\limits_{n}\;\left\lbrack {{\sum\limits_{k}\;{\sum\limits_{m}\;{\varepsilon_{\lbrack{2\; k}\rbrack}\varepsilon_{\lbrack{2\; m}\rbrack}^{*}p_{\lbrack{{2\; n} - {2\; k}}\rbrack}p_{\lbrack{{2\; n} - {2\; m}}\rbrack}^{*}}}} + {\sum\limits_{k}\;{\sum\limits_{m}\;{\varepsilon_{\lbrack{{2\; k} - 1}\rbrack}\varepsilon_{\lbrack{{2\; m} - 1}\rbrack}^{*}p_{\lbrack{{2\; n} - {2\; k} + 1}\rbrack}p_{\lbrack{{2\; n} - {2\; m} + 1}\rbrack}^{*}}}} + {{2 \cdot {Real}}\left\{ {\sum\limits_{k}\;{\sum\limits_{m}\;{\varepsilon_{\lbrack{2\; k}\rbrack}\varepsilon_{\lbrack{{2\; m} - 1}\rbrack}^{*}p_{\lbrack{{2\; n} - {2\; k}}\rbrack}p_{\lbrack{{2\; n} - {2\; m} + 1}\rbrack}^{*}}}} \right\}}} \right\rbrack}} & {{{Eq}.\mspace{14mu} 1}\; C}\end{matrix}$

In Eq. 1C, the first and second summation terms are associated with thedistance of the even-indexed and odd-indexed virtual subcarriersrespectively. Accordingly, one goal in designing a cyclic filterimplementation of ISC generation circuit 104 may be to maximize thefirst and second terms of Eq. 1C. The third term takes on both positiveand negative values depending on the error pattern. In general, thisterm will reduce the minimum distance related to the most-probable errorpatterns. Accordingly, one goal in designing a cyclic filterimplementation of ISC generation circuit 104 may be to minimize thethird term of Eq. 1C (i.e., minimizing cross-correlation between evenand odd virtual subcarriers). Additionally or alternatively, a cyclicfilter implementation of ISC generation circuit 104 may be designed suchthat the first and second terms should have similar levels, which maycorrespond to even-indexed and odd-indexed symbol sequences havecomparable distances (i.e., seeking energy balance between even-indexedand odd-indexed virtual subcarriers).

In presence of frequency-selective fading channel, the inter-subcarriercorrelation created by 104 (by filtering or by matrix multiplication,for example) may be used to overcome the frequency-selective fading andto improve detection performance at the receiver. The processing ofinter-subcarrier correlation may be perceived as “analog interleaving”over the frequency domain that spreads each of the C′ informationsymbols over a plurality of frequency subcarriers. As a result of this“analog interleaving,” a notch in one of the subcarriers will have arelatively low impact on detection, assuming that rest of subcarriersthat are carrying that information symbol are received withsufficiently-high SNR.

In case of frequency selective fading channel, feedback from thereceiving device may be used to dynamically adapt transmissionproperties. An example process for such dynamic adaption is shown inFIG. 3.

In block 302 frequency selective fading is causing a significant notchthat is critically impacting one or more subcarriers. For example, thenotch may be reducing the received SNR of the subcarrier(s) below acertain level (e.g., a level that is predetermined and/oralgorithmically controlled during run time).

In block 304, an identification of such impacted subcarrier(s) may besent from the receiving device to the transmitting device (e.g., over acontrol channel).

In block 306, in response to receiving the indication sent in block 304,the transmitting device disables transmission of data over the impactedsubcarrier(s). The transmitting device may disable transmission of dataover the impacted subcarrier(s) by, for example, reconfiguring themapper 102 (e.g., changing the value of C′ and/or configuring the mapper102 to insert pilot symbols between data symbols), changing p,reconfiguring the decimation circuit 108 (e.g., changing the value ofC), and/or reconfiguring the mapping performed by the serial-to-parallelcircuit 110.

In block 308, the receiving device may determine that data transmissionon the disabled subcarriers should resume.

In block 310, the instruction to resume data transmission on thedisabled subcarrier(s) may be sent (e.g., via a control channel). In anexample implementation, such a determination may be made by monitoringpilot signal(s) that the transmitting device transmits on the disabledsubcarrier(s). For example, the receiving device may monitor acharacteristic (e.g., SNR) of the pilot signal(s) and determine toresume use of the subcarriers(s) upon a significant and/or sustainedchange in the characteristic (e.g., upon SNR of the pilot signal(s)increasing above a determined threshold for a determined amount of time.In an example implementation, the determination to resume datatransmission on the disabled subcarrier(s) may be based on the one ormore characteristics of subcarriers adjacent to the disabledsubcarrier(s). For example, while subcarrier N is disabled, thereceiving device may monitor SNR of adjacent subcarriers N−1 and/or N+1,and may decide enable subcarrier N in response to a significant and/orsustained increase in the SNR of subcarrier(s) N−1 and/or N+1. The firstexample above for SNR estimation of disabled subcarrier(s) which isbased on pilots, may be more accurate than the second example which isbased on SNR estimation using adjacent subcarriers. However, the secondexample does not “waste” power on pilot subcarrier(s) transmission thusmay provide higher power for the information (modulated) subcarriersassuming that the transmitted power is fixed. The relative increasedpower of the modulated subcarriers may improve decoding performance(e.g., SER, BER, packet error rate).

Similarly, feedback from the receiving device (e.g., in the form ofsubcarrier SNR measurements) may be used to adapt the ISC generationcircuit 104 and/or decimation circuit 108. Such adaptation may, forexample, give relatively-high-SNR subcarriers relatively-highcoefficients and relatively-low-SNR subcarriers relatively-lowcoefficients. Such adaptation of coefficients may be used to optimizecommunication capacity (or to achieve a target communication capacity)between the transmitting device and the receiving device. The controlchannel latency and adaptation rate may be controlled to be fast enoughto accommodate channel coherence time.

Returning to FIG. 1B, additional, or alternative, design goals for thecircuit 104 may stem from a desire to reduce complexity of the sequenceestimation in the receiver. As an example, one design goal may be, asdescribed in U.S. patent application Ser. No. 13/754,998, maximizing themagnitude of coefficients of “early” (or low-indexed) taps of a cyclicfilter implementation of circuit 104. As another example, one designgoal may be, as described in U.S. patent application Ser. No.13/754,998, minimizing the cumulative power of the “late” (orhigh-indexed) taps of a cyclic filter implementation of circuit 104.

As shown by the example simulation results in FIG. 1B (compressionfactor=2 used for purposes of illustration), a complex-valued shapingfilter can exploit the full spectrum and make the even-indexed (“ph 1”)and odd-indexed responses (“ph 2”) substantially orthogonal by usingdisjoint parts of the spectrum. FIG. 1B shows an example of thefrequency response of the even-indexed and odd-indexed coefficients of acyclic filter implementation of circuit 104 that was designed inaccordance with this disclosure. Also, shown in the lower portion ofFIG. 1B is the total/combined even and odd response, which, as can beseen, is substantially flat.

Returning to FIG. 1A, the serial-to-parallel circuit 110 may be operableto convert C physical subcarrier values conveyed serially as signal 109to C physical subcarrier values input conveyed in parallels as signals111.

In an example implementation, the subcarrier values output by thedecimation circuit 108 may be interleaved prior to being input to thecircuit 112 and/or the circuit 110 may perform interleaving of theinputted subcarrier values. This interleaver may be operable to improvethe tolerance to frequency selective fading caused by multipath that mayimpose wide notch that spans over several subcarriers. In this case theinterleaver may be used to “spread” the notch over non-consecutive(interleaved) subcarriers and therefore reduce the impact of the notchon decoding performance.

Each of the signals 103, 105, 109, and 111 may be frequency-domainsignals. The inverse fast Fourier transform (IFFT) circuit 112 may beoperable to convert the frequency-domain samples of signals 111 totime-domain samples of signals 113.

The parallel-to-serial circuit 114 may be operable to convert theparallel signals 113 to a serial signal 115.

The circuit 116 may be operable to process the signal 115 to generatethe signal 117. The processing may include, for example, insertion of acyclic prefix. Additionally, or alternatively, the processing mayinclude application of a windowing function to compensate for artifactsthat may result when a receiver of the transmitted signal uses the FFTto recover information carried in the transmitted signal. Windowingapplied the in transmitter 100 may be instead of, or in addition to,windowing applied in a receiver.

The transmitter front-end 118 may be operable to convert the signal 117to an analog representation, upconvert the resulting analog signal, andamplify the upconverted signal to generate the signal 119 that istransmitted into the channel 120. Thus, the transmitter front-end 118may comprise, for example, a digital-to-analog converter (DAC), mixer,and/or power amplifier. The front-end 118 may introduce non-lineardistortion and/or phase noise (and/or other non-idealities) to thesignal 117. The non-linearity of the circuit 118 may be represented asNL_(Tx) which may be, for example, a polynomial, or an exponential(e.g., Rapp model). The non-linearity may incorporate memory (e.g.,Voltera series). In an example implementation, the transmitter 100 maybe operable to transmit its settings that relate to the nonlineardistortion inflicted on transmitted signals by the front-end 118. Suchtransmitted information may enable a receiver to select an appropriatenonlinear distortion model and associated parameters to apply (asdescribed below).

The channel 120 may comprise a wired, wireless, and/or opticalcommunication medium. The signal 119 may propagate through the channel120 and arrive at a receiver such as the receiver described below withrespect to FIG. 2A.

In various example embodiments, subcarrier-dependent bit-loading andtime-varying bit-loading may also be used.

FIG. 1C depicts a flowchart describing operation of an exampleimplementation of a highly-spectrally-efficient OFDM transmitter. Theprocess begins with block 152 in which a baseband bitstream is generated(e.g., by an application running on a smartphone, tablet computer,laptop computer, or other computing device).

In block 154, the baseband bitstream is mapped according to a symbolconstellation. In the example implementation depicted, C′ (an integer)sets of log 2(N) bits of the baseband bitstream are mapped to C′ N-QAMsymbols.

In block 156, the C′ symbols are cyclically convolved, using a filterdesigned as described above with reference to FIG. 1A, to generate C′virtual subcarrier values having a significant, controlled amount ofinter-symbol correlation among symbols to be output on differentsubcarriers.

In block 158, the C′ virtual subcarrier values output by the ISCgeneration circuit 104 may be decimated down to C physical subcarriervalues, each of which is to be transmitted over a respective one of theC+ΔOFDM subcarriers of the channel 120. In an example implementation,the decimation may be by a factor of between approximately 1.25 and 3.

In block 160, the C physical subcarrier values are input to the IFFT anda corresponding C+Δ time-domain values are output for transmission overC+Δ subcarriers of the channel 120.

In block 162, a cyclic prefix may be appended to the C time domainsamples resulting from block 160. A windowing function may also beapplied to the samples after appending the cyclic prefix.

In block 164 the samples resulting from block 162 may be converted toanalog, upconverted to RF, amplified, and transmitted into the channel120 during a OFDM symbol period that is approximately (e.g., withincircuit tolerances) (C+Δ)/BW.

FIG. 2A is a diagram of an example OFDM receiver. The example receiver200 comprises a front-end 202, a cyclic prefix and windowing circuit204, a serial-to-parallel conversion circuit 208, a frequency correctioncircuit 206, a fast Fourier transform (FFT) circuit 210, a per-toneequalizer 212, a phase correction circuit 214, a parallel-to-serialconversion circuit 216, a decoding circuit 218, a controlled combinedinter-symbol correlation (ISC) and/or inter-subcarrier interference(ICI) model (Controlled ISCI Model) circuit 220, a carrier recovery loopcircuit 222, a FEC decoder circuit 232, and a performance indicatormeasurement circuit 234.

The receiver front-end 202 may be operable to amplify, downconvert,and/or digitize the signal 121 to generate the signal 203. Thus, thereceiver front-end 202 may comprise, for example, a low-noise amplifier,a mixer, and/or an analog-to-digital converter. The front-end 202 may,for example, sample the received signal 121 at least C+Δtimes per OFDMsymbol period. Due to non-idealities, the receiver front-end 202 mayintroduce non-linear distortion and/or phase noise to the signal 203.The non-linearity of the front end 202 may be represented as NL_(Rx)which may be, for example, a polynomial, or an exponential (e.g., Rappmodel). The non-linearity may incorporate memory (e.g., Voltera series).

The circuit 204 may be operable to process the signal 203 to generatethe signal 205. The processing may include, for example, removal of acyclic prefix. Additionally, or alternatively, the processing mayinclude application of a windowing function to compensate for artifactsthat may result from use of an FFT on a signal that is not periodic overthe FFT window. Windowing applied in the transmitter 100 may be insteadof, or in addition to, windowing applied in a receiver. The output ofthe circuit 204 may comprise C samples of the received signalcorresponding to a particular OFDM symbol received across C+Δsubcarriers.

The frequency correction circuit 206 may be operable to adjust afrequency of signal 205 to compensate for frequency errors which mayresult from, for example, limited accuracy of frequency sources used forup and down conversions. The frequency correction may be based onfeedback signal 223 from the carrier recovery circuit 222.

The serial-to-parallel conversion circuit 208 may be operable to convertC time-domain samples output serially as the signal 207 to C time-domainsamples output in parallel as signals 209.

In an example implementation, where interleaving of the subcarriervalues was performed in transmitter, the phase/frequency-corrected,equalized subcarrier values output at link 215 may be de-interleavedprior to being input to the circuit 218 and/or the circuit 216 mayperform de-interleaving of the subcarrier values. In this case theControlled ISCI Model 220 (comprising the combined ISC model used by themodulator and/or ICI model reflecting the channel non-idealities) shouldconsider the interleaving operation.

Each of the signals 203, 205, 207, and 209 may be time-domain signals.The fast Fourier transform (FFT) circuit 210 may be operable to convertthe time-domain samples conveyed as signals 209 to C physical subcarriervalues conveyed as signals 211.

The per-tone equalizer 212 may be operable to perform frequency-domainequalization of each of the C physical subcarrier values to compensatefor non-idealities (e.g., multipath, additive white Gaussian noise,(AWGN), etc.) experienced by a corresponding one of the C OFDMsubcarriers. In an example implementation, the equalization may comprisemultiplying a sample of each of signals 211 by a respective one of Ccomplex coefficients determined by the equalization circuit 212. Suchcoefficients may be adapted from OFDM symbol to OFDM symbol. Adaption ofsuch coefficients may be based on decisions of decoding circuit 218. Inan example implementation, the adaptation may be based on an errorsignal 221 defined as the difference, output by circuit 230, between theequalized and phase-corrected samples of signal 217 and thecorresponding reconstructed signal 227 b output by the decoding circuit218. Generation of the reconstructed signal 227 b may be similar togeneration of the reconstructed signal 203 in the above-incorporatedU.S. patent application Ser. No. 13/754,964 (but modified for the OFDMcase, as opposed to the single-carrier case described therein) and/or asdescribed below with reference to FIG. 2D.

The phase correction circuit 214 may be operable to adjust the phase ofthe received physical subcarrier values. The correction may be based onthe feedback signal 225 from the carrier recovery circuit 222 and maycompensate for phase errors introduced, for example, by frequencysources in the front-end of the transmitter and/or the front-end 202 ofthe receiver.

The parallel-to-serial conversion circuit 216 may convert the C physicalsubcarrier values output in parallel by circuit 214 to a serialrepresentation. The physical subcarrier values bits may then be conveyedserially to the decoding circuit 218. Alternatively, 216 may be bypassed(or not present) and the decoding at 218 may be done iteratively overthe parallel (vector) signal 215.

The controlled ISCI model circuit 220 may be operable to store tapcoefficients p and/or nonlinearity model {circumflex over(N)}{circumflex over (L)} The stored values may, for example, have beensent to the receiver 200 by the transmitter 100 in one or more controlmessages. The controlled ISCI model circuit 220 may be operable toconvert a time-domain representation of a nonlinearity model to afrequency domain representation. The model 220 may, for example, store(e.g., into a look-up table) multiple sets of filter coefficients and/ornonlinearity models and may be operable to dynamically select (e.g.,during operation based on recent measurements) the most appropriateone(s) for the particular circumstances.

The decoding circuit 218 may be operable to process the signal 217 torecover symbols carried therein. In an example implementation, thedecoding circuit 218 may be an iterative maximum likelihood or maximum apriori decoder that uses symbol slicing or other techniques that enableestimating individual symbols rather than sequences of symbols. Inanother example implementation, the decoding circuit 218 may be asequence estimation circuit operable to perform sequence estimation todetermine the C′ symbols that were generated in the transmittercorresponding to the received OFDM symbol. Such sequence estimation maybe based on maximum likelihood (ML) and/or maximum a priori (MAP)sequence estimation algorithm(s), including reduced-complexity (e.g.,storing reduced channel state information) versions thereof. Thedecoding circuit 218 may be able to recover the C′ symbols from the Cphysical subcarriers (where C′>C) as a result of the controlledinter-symbol correlation and/or aliasing that was introduced by thetransmitter (e.g., as a result of the processing by the ISC generationcircuit 104 and/or the aliasing introduced by the decimation circuit108). The decoding circuit 218 may receive, from circuit 220, afrequency-domain controlled ISCI model which may be based onnon-linearity, phase noise, and/or other non-idealities experienced byone or more of the C physical subcarrier values arriving at the decodingcircuit 218.

The decoding circuit 218 may use the controlled ISCI model to calculatemetrics similar to the manner in which a model is used to calculatemetrics in above-incorporated U.S. patent application Ser. No.13/754,964 (but modified for the OFDM case as opposed to thesingle-carrier case described therein) and/or as described below withreference to FIG. 2C. The decoding circuit 218 may also use thecontrolled ISCI model provided by circuit 220 to generate signals 227 aand 227 b, as described herein. In an example implementation, thedecoding circuit 218 is operable to get at its input C equalized andphase-corrected physical subcarrier values and generate LLR valuesassociated with the bits of the C′ constellation symbols that whereoriginally loaded over the virtual subcarriers of the WAM-OFDMtransmitter. The LLRs may be generated by checking multiple hypothesesof C′ constellation symbols based on the received samples. The besthypothesis may be used to generate the symbols and hard bits detection.In case of using a soft error correction code, an LLR interface thatreflects the reliability of the bits (analog signal) rather than thehard bits (i.e., “0”, “1”) may be used. A remaining one or more of thehypotheses (the second-best, third-best, etc.) may be used to generatethe LLR values. For example, assuming that a particular bit was detectedas “1” according to the best hypothesis, the LLR for this bit may beprovided from the distance of the best hypothesis to the second besthypothesis that estimates this particular bit as “0”. The LLR values forthe different virtual subcarriers may be weighted according to theirrespective SNR. In case of frequency-selective fading channel, eachsubcarrier may have a different gain that corresponds to a different SNRper subcarrier. Because LLR value reflects the bit reliability, in anexample implementation, the LLRs may be weighted according to theappropriate subcarrier gain to achieve Maximum Likelihood performance.In an example implementation, log-likelihood ratios (LLRs) determined ina receiver (e.g., in circuit 218) may have a noise variance componentthat varies with subcarrier. This may be because the per-subcarrierchannel gain (due, for example, to the analog channel selection filtercircuits and channel) may vary with frequency but the RF front-end gainat the receiver may be fixed.

For each received OFDM symbol, the circuit 220 may generate afrequency-domain controlled ISCI model of the channel over which theOFDM symbol was received. The controlled ISCI model of 220 may accountfor non-linear distortion experienced by the received OFDM symbol, phasenoise experienced by the received OFDM symbol, and/or othernon-idealities. For example, a third-order time domain distortion may bemodeled in the frequency domain as:

y(t) = x(t) ⋅ (1 − r ⋅ 𝕖^(jφ) ⋅ x(t)²) = x(t) − r ⋅ 𝕖^(jφ) ⋅ x(t) ⋅ x^(*)(t) ⋅ x(t)Y(ω) = X(ω) − r ⋅ 𝕖^(jφ) ⋅ X(ω) ⊗ X^(*)(−ω) ⊗ X(ω),where:

x(t), X(ω)—are the input signal in the time domain and frequency domain,respectively;

y(t), Y(ω)—are the distorted output signal in the time domain andfrequency domain, respectively;

r·e^(jφ)—is the complex distortion coefficients;

( )*—denotes complex conjugate operator; and

—stands for the convolution operator.

The carrier recovery loop circuit 222 may be operable to recover phaseand frequency of one or more of the C OFDM subcarriers of the channel120. The carrier recovery loop 222 may generate a frequency error signal223 and a phase error signal 225. The phase and/or frequency error maybe determined by comparing physical subcarrier values of signal 217 to areconstructed signal 227 a. Accordingly, the frequency error and/orphase error may be updated from OFDM symbol to OFDM symbol. Thereconstructed signal 227 b may be generated similar to the manner inwhich the reconstructed signal 207 of the above-incorporated U.S. patentapplication Ser. No. 13/754,964 (but modified for the OFDM case, asopposed to the single-carrier case described therein) and/or asdescribed below with reference to FIG. 2D.

The performance indicator measurement circuit 234 may be operable tomeasure, estimate, and/or otherwise determine characteristics ofreceived signals and convey such performance measurement indications toa transmitter collocated with the receiver 200 for transmitting thefeedback to the remote side. Example performance indicators that thecircuit 234 may determine and/or convey to a collocated transmitter fortransmission of a feedback signal include: signal-to-noise ratio (SNR)per subcarrier (e.g., determined based on frequency-domain values at theoutput of FFT 210 and corresponding decisions at the output of thedecoding circuit 218 and/or FEC decoder 232), symbol error rate (SER)(e.g., measured by decoding circuit 218 and conveyed to the circuit234), and/or bit error rate (BER) (e.g., measured by the FEC decoder andconveyed to the circuit 234).

FIGS. 2B and 2C depict a flowchart describing operation of an exampleimplementation of a highly-spectrally-efficient OFDM receiver. Theprocess begins with block 242 in which an OFDM symbol arrives, as signal121, at front-end 202 and is amplified, down-converted, and digitized togenerate C+Δ+P time-domain samples of the OFDM symbol, where P is thesize of the cyclic prefix.

In block 244, the cyclic prefix may be removed and a windowing functionmay be applied.

In block 246, frequency correction may be applied to the time-domainsamples based on an error signal 223 determined by the carrier recoverycircuit 222.

In block 248, the frequency-corrected time-domain samples are convertedto frequency-corrected frequency-domain physical subcarrier values bythe FFT circuit 210.

In block 250, the frequency-corrected physical subcarrier values outputby the FFT are equalized in the frequency domain by the per-subcarrierequalizer circuit 212.

In block 252, one or more of the frequency-corrected and equalizedphysical subcarrier values are phase corrected based on a phasecorrection signal 225 generated by the carrier recovery circuit 222.

In block 254, the vector of C frequency-corrected, equalized, andphase-corrected received physical subcarrier values is input to decodingcircuit 218 and sequence estimation is used to determine the bestestimates of the vector of C′ symbols that resulted in the vector of Cfrequency-corrected, equalized, and phase-corrected received physicalsubcarrier values. Example details of metric generation performed duringthe sequence estimation are described below with reference to FIG. 2C.

In block 256, the best estimate of the vector of C′ symbols isdetermined by decoding circuit 218 and is output as signal 219 to FECdecoder 232, which outputs corrected values on signal 233. Exampledetails of selecting the best candidate vector are described below withreference to FIG. 2C.

Referring to FIG. 2C, in block 262, the decoding circuit 218 generates aplurality of candidate vectors (each candidate vector corresponding to apossible value of the vector of C′ symbols generated by thetransmitter), and generates a corresponding plurality of reconstructedphysical subcarrier vectors by applying the controlled ISCI model to thecandidates.

In block 264, the reconstructed physical subcarrier vectors are comparedto the vector of frequency-corrected, equalized, and/or phase-correctedreceived physical subcarrier values to calculate metrics.

In block 266, the candidate vector corresponding to the best metric isselected as the best candidate, and the C′ symbols of the best candidateare output as signal 219, to, for example, FEC decoder 232 and/or aninterleaver (not shown).

FIG. 2D depicts a flowchart describing operation of an example decodingcircuit of a highly-spectrally-efficient OFDM receiver. The flowchartbegins with block 272 in which a vector of C received physicalsubcarrier values arrive at decoding circuit 218.

In block 274, the best candidate vector is determined to a first levelof confidence. For example, in block 274, the best candidate vector maybe determined based on a first number of iterations of a sequenceestimation algorithm.

In block 276, the controlled ISCI model may be applied to the bestcandidate vector determined in block 274 to generate reconstructedsignal 227 a.

In block 278, the best candidate vector is determined to a second levelof confidence. For example, the best candidate determined in block 278may be based on a second number of iterations of the sequence estimationalgorithm, where the second number of iterations is larger than thefirst number of iterations.

In block 280, the controlled ISCI model may be applied to the bestcandidate determined in block 278 to generate reconstructed signal 227b.

In block 282, coefficients used by the equalizer 212 are updated/adaptedbased on the reconstructed signal 227 b determined in block 280.

In block 284, subsequent received physical subcarrier values areequalized based on the coefficients calculated in block 282.

Blocks 286 and 288 may occur in parallel with blocks 278-284.

In block 286, the carrier recovery loop 222 may determine frequencyand/or phase error based on signal 227 a calculated in block 276.

In block 288, samples received during a subsequent OFDM symbol periodmay be frequency corrected based on the error determined in block 286and/or subsequent received physical subcarrier values are phasecorrected based on the error determined in block 286.

In an example implementation, a first electronic device (e.g., 100), maymap, using a selected modulation constellation, each of C′ bit sequencesto a respective one of C′ symbols, where C′ is a number greater thanone. The electronic device may process the C′ symbols to generate C′inter-carrier correlated virtual subcarrier values. The electronicdevice may decimate the C′ virtual subcarrier values down to C physicalsubcarrier values, C being a number less than C′. The electronic devicemay transmit the C physical subcarrier values on C orthogonal frequencydivision multiplexed (OFDM) subcarriers. The transmission may be via achannel having a significant amount of nonlinearity. The significantamount of nonlinearity may be such that it degrades, relative to aperfectly linear channel, a performance metric in said receiver by lessthan 1 dB, whereas, in a full response communication system, it woulddegrade, relative to a perfectly linear channel, the performance metricby 1 dB or more. The processing may introduce a significant amount ofaliasing such that the ratio of the signal power of the C′ virtualsubcarrier values prior to the decimating to the signal power of the Cphysical subcarrier values after the decimating is equal to or less thana threshold signal to noise ratio of a receiver to which the OFDMsubcarriers are transmitted (e.g., for a decimation by a factor of 2, P2is the power in the upper half of the C′ virtual subcarrier values). Themodulation constellation may be an N-QAM constellation, N being aninteger. The bit sequences may be coded according to a forward errorcorrection algorithm. The processing may comprise multiplication of C′symbols by a C′×C′ matrix. Row or column length of the matrix may be aninteger less than C′, such that the multiplication results in adecimation of the C′ symbols. The processing may seeks to achieve atarget symbol error rate, target bit error rate, and/or target packeterror rate in presence of additive white Gaussian noise and a dynamicfrequency selective fading channel. The processing may comprisesfiltering the C′ symbols using an array of filter tap coefficients. Thefiltering may comprise cyclic convolution. The filtering may comprisesmultiplication by a circulant matrix populated with the filter tapcoefficients. The filter tap coefficients may be selected to achieve oneor more of: a target symbol error rate, a target bit error rate, and/ora target packet error rate in presence of one or more of: additive whiteGaussian noise, dynamic frequency selective fading channel, andnon-linear distortion. The filter tap coefficients may be selected basedon signal-to-noise ratio (SNR) measurements fed back from a secondelectronic device that receives communications from the first electronicdevice.

The electronic device may receive a first message from a secondelectronic device. In response to the first message, the firstelectronic device may cease transmission of data on a particular one ofthe physical subcarriers. The electronic device may receive a secondmessage from the second electronic device. In response to the secondmessage, the first electronic device may resume transmission of data onthe particular one of the physical subcarriers. Subsequent to thereceiving the first message, and prior to receiving the second message,transmitting a pilot signal on the particular one of the physicalsubcarriers. The ceasing transmission of data on the particular one ofthe physical subcarriers may comprise one or more of: changing a valueof the number C; and changing a value of the number C′. An OFDM symbolperiod for the transmitting may be approximately (C+Δ)/BW. Each of the COFDM subcarriers has a bandwidth of approximately BW/(C+Δ), where BW isa bandwidth used for the transmitting, and Δ is the number ofnon-data-carrying subcarriers within the bandwidth BW. Prior to thetransmitting, transforming the C physical subcarrier values to C+Δ+Ptime-domain samples using an inverse fast Fourier transform.

Other implementations may provide a non-transitory computer readablemedium and/or storage medium, and/or a non-transitory machine readablemedium and/or storage medium, having stored thereon, a machine codeand/or a computer program having at least one code section executable bya machine and/or a computer, thereby causing the machine and/or computerto perform the processes as described herein.

Methods and systems disclosed herein may be realized in hardware,software, or a combination of hardware and software. Methods and systemsdisclosed herein may be realized in a centralized fashion in at leastone computing system, or in a distributed fashion where differentelements are spread across several interconnected computing systems. Anykind of computing system or other apparatus adapted for carrying out themethods described herein is suited. A typical combination of hardwareand software may be a general-purpose computing system with a program orother code that, when being loaded and executed, controls the computingsystem such that it carries out methods described herein. Anothertypical implementation may comprise an application specific integratedcircuit (ASIC) or chip with a program or other code that, when beingloaded and executed, controls the ASIC such that is carries out methodsdescribed herein.

While methods and systems have been described herein with reference tocertain implementations, it will be understood by those skilled in theart that various changes may be made and equivalents may be substitutedwithout departing from the scope of the present method and/or system. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the present disclosure without departingfrom its scope. Therefore, it is intended that the present method and/orsystem not be limited to the particular implementations disclosed, butthat the present method and/or system will include all implementationsfalling within the scope of the appended claims.

What is claimed is:
 1. A method performed in a first electronic device,the method comprising: mapping, using a modulation constellation, eachof C′ bit sequences to a respective one of C′ symbols, where C′ is anumber greater than one; processing said C′ symbols to generate C′inter-carrier correlated virtual subcarrier values; decimating said C′virtual subcarrier values down to C physical subcarrier values, C beingan number less than C′; transmitting said C physical subcarrier valueson C orthogonal frequency division multiplexed (OFDM) subcarriers;receiving a first message from a second electronic device; in responseto said first message, ceasing transmission of data on a particular oneof said OFDM subcarriers; receiving a second message from said secondelectronic device; and in response to said second message, resumingtransmission of data on said particular one of said OFDM subcarriers. 2.The method of claim 1, wherein: said transmitting is via a channelhaving a significant amount of nonlinearity; said significant amount ofnonlinearity degrades a performance metric in a receiver by less than 1dB, relative to a perfectly linear channel; and in a full responsecommunication system, said significant amount of nonlinearity woulddegrade said performance metric by 1 dB or more, relative to a perfectlylinear channel.
 3. The method of claim 1, wherein said modulationconstellation is an N-QAM constellation, N being an integer.
 4. Themethod of claim 1, wherein said bit sequences are coded according to aforward error correction algorithm.
 5. The method of claim 1, whereinsaid processing comprises multiplication of said C′ symbols by a C′×C′matrix.
 6. The method of claim 1, wherein said processing comprisesfiltering said C′ symbols using an array of filter tap coefficients. 7.The method of claim 6, wherein said filtering comprises cyclicconvolution.
 8. The method of claim 7, wherein said filtering comprisesmultiplication by a circulant matrix populated with said filter tapcoefficients.
 9. The method of claim 6, wherein said filter tapcoefficients are selected based on signal-to-noise ratio (SNR)measurements fed back from said second electronic device that receivescommunications from said first electronic device.
 10. The method ofclaim 1, comprising: subsequent to said receiving said first message andprior to receiving said second message, transmitting a pilot signal onsaid particular one of said physical subcarriers.
 11. The method ofclaim 1, wherein said ceasing transmission of data on said particularone of said physical subcarriers comprises one or more of: changing avalue of said number C; and changing a value of said number C′.
 12. Themethod of claim 1, wherein: an OFDM symbol period for said transmittingis approximately (C+Δ)/BW; and each of said C OFDM subcarriers has abandwidth of approximately BW/(C+Δ), where BW is a bandwidth used forsaid transmitting, and Δ is the number of non-data-carrying OFDMsubcarriers within said bandwidth BW.
 13. The method of claim 1,comprising, prior to said transmitting, transforming said C physicalsubcarrier values to C+Δ+P time-domain samples using an inverse fastFourier transform, where Δ is the number of non-data-carrying OFDMsubcarriers and P is cyclic prefix size.
 14. A method performed in afirst electronic device, the method comprising: mapping, using amodulation constellation, each of C′ bit sequences to a respective oneof C′ symbols, where C′ is a number greater than one; processing said C′symbols to generate C′ inter-carrier correlated virtual subcarriervalues; decimating said C′ virtual subcarrier values down to C physicalsubcarrier values, where C is a number less than C′; transmitting said Cphysical subcarrier values on C orthogonal frequency divisionmultiplexed (OFDM) subcarriers, wherein: said processing comprisesmultiplication of said C′ symbols by a matrix; and row or column lengthof said matrix is an integer less than C′, such that said multiplicationresults in said decimating of said C′ symbols.
 15. A method performed ina first electronic device, the method comprising: mapping, using amodulation constellation, each of C′ bit sequences to a respective oneof C′ symbols, where C′ is a number greater than one; processing said C′symbols to generate C′ inter-carrier correlated virtual subcarriervalues; decimating said C′ virtual subcarrier values down to C physicalsubcarrier values, where C is a number less than C′; transmitting said Cphysical subcarrier values on C orthogonal frequency divisionmultiplexed (OFDM) subcarriers; and configuring said processing based onfeedback indicating a symbol error rate, bit error rate, and/or packeterror rate, wherein said configuring seeks to achieve a target symbolerror rate, target bit error rate, and/or target packet error rate inpresence of additive white Gaussian noise and a dynamic frequencyselective fading channel.
 16. A method performed in a first electronicdevice, the method comprising: mapping, using a modulationconstellation, each of C′ bit sequences to a respective one of C′symbols, where C′ is a number greater than one; processing said C′symbols to generate C′ inter-carrier correlated virtual subcarriervalues, wherein said processing comprises filtering said C′ symbolsusing an array of filter taps; decimating said C′ virtual subcarriervalues down to C physical subcarrier values, where C is a number lessthan C′; transmitting said C physical subcarrier values on C orthogonalfrequency division multiplexed (OFDM) subcarriers, wherein saidfiltering comprises cyclic convolution; and selecting said filter tapcoefficients based on feedback indicating a symbol error rate, bit errorrate, and/or packet error rate, wherein said selecting seeks to achieveone or more of: a target symbol error rate, a target bit error rate,and/or a target packet error rate in presence of one or more of:additive white Gaussian noise, dynamic frequency selective fadingchannel, and non-linear distortion.
 17. An electronic device comprising:a filter circuit operable to process a quantity, C′, of symbols togenerate C′ virtual subcarrier values, wherein there is inter-carriercorrelation among said C′ virtual subcarriers values, and C′ is anumber; a decimation circuit operable to decimate said C′ virtualsubcarrier values down to C physical subcarrier values, wherein C is anumber less than C′; a transform circuit operable transform said Cphysical subcarrier values to C+Δ+P time-domain samples, where Δ is thenumber of non-data-carrying OFDM subcarriers and P is cyclic prefixsize; a front-end circuit operable to transmit said time-domain samplesinto a channel, wherein: said filter circuit is configured to perform acyclic convolution of said C′ symbols; said cyclic convolution comprisesmultiplication by a circulant matrix populated with filter tapcoefficients and zeros; and said decimation is realized by saidcirculant matrix having a dimension less than C′.
 18. The electronicdevice of claim 17, wherein each of said C′ symbols is an N-QAM symbol,N being an integer.
 19. The electronic device of claim 17, wherein saidelectronic device is operable to transmit tap coefficients of saidfilter circuit to a receiver.
 20. The electronic device of claim 17,wherein said electronic device is operable to transmit coefficients ofsaid filter circuit such that a receiver may receive the coefficientsand update its controlled combined inter-symbol correlation and/orinter-subcarrier interference (ISCI) model.
 21. The electronic device ofclaim 17, wherein said electronic device is operable to transmitsettings of said front-end circuit that enable a receiver to determine anonlinear distortion model.
 22. An electronic device comprising: afilter circuit operable to process a quantity, C′, of symbols togenerate C′ virtual subcarrier values, wherein: there is inter-carriercorrelation among said C′ virtual subcarriers values, and C′ is anumber; and said filter circuit is operable to select said filter tapcoefficients based on feedback indicating one or more of symbol errorrate, bit error rate, and/or packet error rate to achieve one or moretarget performance metrics in presence of additive white Gaussian noiseand a dynamic frequency selective fading channel; a decimation circuitoperable to decimate said C′ virtual subcarrier values down to Cphysical subcarrier values, where C is a number less than C′; atransform circuit operable transform said C physical subcarrier valuesto C+Δ+P time-domain samples, where Δ is a number equal to the number ofnon-data-carrying subcarriers and P is cyclic prefix size; and afront-end circuit operable to transmit said time-domain samples into achannel.
 23. An electronic device comprising: a filter circuit operableto process a quantity, C′, of symbols to generate C′ virtual subcarriervalues, wherein there is inter-carrier correlation among said C′ virtualsubcarriers values, and C′ is a number; a decimation circuit operable todecimate said C′ virtual subcarrier values down to C physical subcarriervalues, where C is a number less than C′; a transform circuit operabletransform said C physical subcarrier values to C+Δ+P time-domainsamples, where Δ is the number of non-data-carrying OFDM subcarriers andP is cyclic prefix size; and a front-end circuit operable to transmitsaid time-domain samples into a channel, wherein said electronic deviceis operable to: in response to a first message from a second electronicdevice, cease transmission of data on a particular one of said OFDMsubcarriers; and in response to a second message from said secondelectronic device, resume transmission of data on said particular one ofsaid OFDM subcarriers.
 24. The electronic device of claim 23, whereinsaid electronic device is operable to, subsequent to said cessation oftransmission of data on said particular one of said physical subcarriersand prior to resuming transmission of data on said particular one ofsaid physical subcarriers, transmit a pilot signal on said particularone of said physical subcarriers.